Zwitterionic or Not? Fast and Reliable Structure Determination by Combining Crystal Structure Prediction and Solid-State NMR

When it comes to crystal structure determination, computational approaches such as Crystal Structure Prediction (CSP) have gained more and more attention since they offer some insight on how atoms and molecules are packed in the solid state, starting from only very basic information without diffraction data. Furthermore, it is well known that the coupling of CSP with solid-state NMR (SSNMR) greatly enhances the performance and the accuracy of the predictive method, leading to the so-called CSP-NMR crystallography (CSP-NMRX). In this paper, we present the successful application of CSP-NMRX to determine the crystal structure of three structural isomers of pyridine dicarboxylic acid, namely quinolinic, dipicolinic and dinicotinic acids, which can be in a zwitterionic form, or not, in the solid state. In a first step, mono- and bidimensional SSNMR spectra, i.e., 1H Magic-Angle Spinning (MAS), 13C and 15N Cross Polarisation Magic-Angle Spinning (CPMAS), 1H Double Quantum (DQ) MAS, 1H-13C HETeronuclear CORrelation (HETCOR), were used to determine the correct molecular structure (i.e., zwitterionic or not) and the local molecular arrangement; at the end, the RMSEs between experimental and computed 1H and 13C chemical shifts allowed the selection of the correct predicted structure for each system. Interestingly, while quinolinic and dipicolinic acids are zwitterionic and non-zwitterionic, respectively, in the solid state, dinicotinic acid exhibits in its crystal structure a “zwitterionic-non-zwitterionic continuum state” in which the proton is shared between the carboxylic moiety and the pyridinic nitrogen. Very refined SSNMR experiments were carried out, i.e., 14N-1H Phase-Modulated (PM) pulse and Rotational-Echo Saturation-Pulse Double-Resonance (RESPDOR), to provide an accurate N–H distance value confirming the hybrid nature of the molecule. The CSP-NMRX method showed a remarkable match between the selected structures and the experimental ones. The correct molecular input provided by SSNMR reduced the number of CSP calculations to be performed, leading to different predicted structures, while RMSEs provided an independent parameter with respect to the computed energy for the selection of the best candidate.


Introduction
In crystal engineering, single-crystal X-ray diffraction (SCXRD) is definitely the most used technique for the determination of crystal structures, even if structure determination from powder data, via direct-space methods or more sophisticated methods, like fit to the pair distribution function (PDF) [1], have become more and more reliable. In cases where these techniques may be unfeasible, predicting how molecules will pack in space becomes crucial. Despite many efforts, this often proves to be quite a hard task and represents a The crystal structures of these systems, solved by single-crystal X-ray diffraction (SCXRD) at different temperatures, were already reported in literature (Figure 1a-c), while no polymorphs are known.
QA (Figure 1a, space group P21/c (14), Z' = 1, CSD refcode QUICNA10) crystallises in the zwitterionic form [32], with the transfer of the carboxylic hydrogen to the pyridinic nitrogen. This was confirmed by performing SCXRD analyses at both ambient and low temperatures (100, 80 and 35 K) [33]. In the crystal structure of QA, the molecules are arranged in layers ( Figure 1d); each molecule on the same plane is connected to the others by N + -H•••O − intermolecular hydrogen bonds between adjacent carboxylic groups (O-N distance = 2.725 Å). The crystal structures of these systems, solved by single-crystal X-ray diffraction (SCXRD) at different temperatures, were already reported in literature (Figure 1a-c), while no polymorphs are known.
QA (Figure 1a, space group P2 1 /c (14), Z = 1, CSD refcode QUICNA10) crystallises in the zwitterionic form [32], with the transfer of the carboxylic hydrogen to the pyridinic nitrogen. This was confirmed by performing SCXRD analyses at both ambient and low temperatures (100, 80 and 35 K) [33]. In the crystal structure of QA, the molecules are arranged in layers ( Figure 1d); each molecule on the same plane is connected to the others by N + -H···O − intermolecular hydrogen bonds between adjacent carboxylic groups (O-N distance = 2.725 Å).
DPA (Figure 1b, space group P2 1 /m (11), Z = 1, CSD refcode AFEBUI) shows instead a non-zwitterionic character in the solid state [34]. In the crystal structure of DPA, the molecules are arranged with a ribbon-like shape (Figure 1e). The molecules are connected in infinite chains by homosynthonic hydrogen bonds, R 2 2 (8), between adjacent carboxylic groups (O···O distance = 2.625 Å).  (11), Z' = 1, CSD refcode AFEBUI) shows instead a non-zwitterionic character in the solid state [34]. In the crystal structure of DPA, the molecules are arranged with a ribbon-like shape (Figure 1e). The molecules are connected in infinite chains by homosynthonic hydrogen bonds, (8), between adjacent carboxylic groups (O•••O distance = 2.625 Å). Regarding DNic (Figure 1c, space group P21/c (14), Z' = 1, CSD refcode DINICA12), neutron diffraction (ND) experiments at room temperature (RT) revealed that DNic seems to be in a "continuum" state, with the proton shared between the carboxyl and the nitrogen [35]. At a very low temperature (15 K, CSD refcode DINICA11) [36] the proton moves towards the pyridinic nitrogen, resulting in a more pronounced, but still not complete, zwitterionic form. In the crystal structures of DNic, the molecules lie in parallel planes. On the same plane (Figure 1f), they are connected by two kinds of hydrogen bonds: one between two carboxylic groups (O•••O distance = 2.594 Å at RT) and one between a carboxylic group and the pyridinic nitrogen, N•••H•••O (O•••N distance = 2.515 Å at RT), forming an (24) hydrogen-bonded ring.
The analysis of these systems by means of SSNMR proved crucial to determine the protonation state, which was used as a constraint in the CSP calculations and led to the successful prediction of the crystal structures of QA, DPA and DNic. Regarding DNic (Figure 1c, space group P2 1 /c (14), Z = 1, CSD refcode DINICA12), neutron diffraction (ND) experiments at room temperature (RT) revealed that DNic seems to be in a "continuum" state, with the proton shared between the carboxyl and the nitrogen [35]. At a very low temperature (15 K, CSD refcode DINICA11) [36] the proton moves towards the pyridinic nitrogen, resulting in a more pronounced, but still not complete, zwitterionic form. In the crystal structures of DNic, the molecules lie in parallel planes. On the same plane (Figure 1f), they are connected by two kinds of hydrogen bonds: one between two carboxylic groups (O···O distance = 2.594 Å at RT) and one between a carboxylic group and the pyridinic nitrogen, N···H···O (O···N distance = 2.515 Å at RT), forming an R 4 4 (24) hydrogen-bonded ring. The analysis of these systems by means of SSNMR proved crucial to determine the protonation state, which was used as a constraint in the CSP calculations and led to the successful prediction of the crystal structures of QA, DPA and DNic. This paper addresses the following key points and novelties: -The development of a method for rapid determination of crystal structures of possible zwitterionic systems, with the extent of applicability of this approach being nonetheless much broader than that of zwitterionic systems, since it covers, in general, organic, organometallic and inorganic compounds for which the crystal structure is not available and which have uncertain proton positions; - The unambiguous elucidation of the zwitterionic character of the three structural isomers of pyridine dicarboxylic acid; Molecules 2023, 28, 1876 The evaluation of the "zwitterionic-non-zwitterionic continuum state" in dinicotinic acid with very accurate NMR measurements of the N-H distance. Also in this case, the method can be easily applied to other known situations, such as, for instance, the "salt-cocrystal continuum".

SSNMR Analysis: Zwitterionic Character
QA, DPA and DNic were firstly analysed by SSNMR, to collect information about the content of the unit cell, such as the value of Z and the zwitterionic character (i.e., protonation state of carboxylic and pyridinic groups). This NMR analysis has contributed enormously to identify the correct structure to submit for the CSP calculations. Mono-( 1 H MAS, 13 C and 15 N CPMAS) and bidimensional ( 1 H-13 C short-and long-range HETCOR, 1 H DQ MAS) experiments were conducted at room temperature for all samples (see Table S1 in the Supplementary Materials for all experimental parameters). For convenience, also the comparisons among 1 H, 13 C and 15 N spectra are reported separately in the Supplementary Materials, Figures S1-S3, respectively. The 1 H, 13 C and 15 N SSNMR chemical shifts are well known to be quite sensitive to protonic transfer, in particular for the heteronuclei ( 13 C and 15 N) in carboxylic and pyridinic moieties involved in the resulting hydrogen bonds [37]. The presence of hydrogen bonds in the crystals was assessed by 1 H MAS spectra; indeed, in general, all hydrogen-bonded 1 H chemical shifts appear to be higher for shorter distances between heavy atoms (i.e., stronger hydrogen bonds) and vice versa, in agreement with the literature [37][38][39]. All chemical shifts ( 1 H, 13 C and 15 N) are reported in detail in the Supplementary Materials (Tables S2-S4) while the comparisons between chemical shifts and distances between heavy atoms are reported in Table 1.  Figure 2) of QA clearly report the presence of only one independent molecule in the unit cell (Z = 1), since they are characterised by only one set of signals (i.e., seven peaks out of seven expected in the 13 C spectrum and 1 peak out of 1 expected for the 15 N spectrum). Specifically, in the 13 C CPMAS spectrum, the resonances at 160.4 and 165.3 ppm are ascribable to carboxylic groups and, in particular, the resonance at lower ppm values is typical of a free neutral COOH group, while that at higher frequencies accounts for a deprotonated (COO − ) group, or a neutral group possibly involved in a hydrogen bond.
In the 1 H MAS spectrum, the hydrogen-bond region (above 10 ppm) is characterised by one signal at 14.7 ppm (H1) and another one at 20.4 ppm (H8); the former is consistent with a pyridinium proton involved in a hydrogen bond of intermediate strength, the latter with the presence of a COOH group involved in very strong hydrogen bonds, usually an intramolecular interaction [37][38][39]; this agrees with both the intramolecular hydrogen bond between carboxylic groups present in the experimental crystal structure of the system and the short distance between heavy atoms (see Table 1).
To further validate the presence of a hydrogen bond for the pyridinic moiety and investigate its protonation state, we also acquired a 15 N CPMAS spectrum of QA. It clearly shows a signal at 205.3 ppm, characteristic of a protonated pyridinic nitrogen, i.e., about 100 ppm lower in frequency with respect to that of the free pyridinic nitrogen (around 300-320 ppm, see DPA below) [37]. Molecules 2023, 28, x 6 of 26 In the 1 H MAS spectrum, the hydrogen-bond region (above 10 ppm) is characterised by one signal at 14.7 ppm (H1) and another one at 20.4 ppm (H8); the former is consistent with a pyridinium proton involved in a hydrogen bond of intermediate strength, the latter with the presence of a COOH group involved in very strong hydrogen bonds, usually an intramolecular interaction [37][38][39]; this agrees with both the intramolecular hydrogen bond between carboxylic groups present in the experimental crystal structure of the system and the short distance between heavy atoms (see Table 1).
To further validate the presence of a hydrogen bond for the pyridinic moiety and investigate its protonation state, we also acquired a 15 N CPMAS spectrum of QA. It clearly shows a signal at 205.3 ppm, characteristic of a protonated pyridinic nitrogen, i.e., about 100 ppm lower in frequency with respect to that of the free pyridinic nitrogen (around 300-320 ppm, see DPA below) [37].
This aggregated information, clearly encoded in the SSNMR spectra, shows that QA is in a zwitterionic form in its crystal structure. However, the position of the carboxylate group on the ring was still unclear, since it could be either in the ortho (C2) or meta (C3) positions relative to the pyridinic N. Thus, 2D short-( Figure S4 in the Supplementary Materials) and long-range ( Figure 3a) 1 H-13 C FSLG HETCOR spectra were performed to univocally define the assignment of 13 C signals. This aggregated information, clearly encoded in the SSNMR spectra, shows that QA is in a zwitterionic form in its crystal structure. However, the position of the carboxylate group on the ring was still unclear, since it could be either in the ortho (C2) or meta (C3) positions relative to the pyridinic N. Thus, 2D short-( Figure S4 in the Supplementary Materials) and long-range (Figure 3a) 1 H-13 C FSLG HETCOR spectra were performed to univocally define the assignment of 13 C signals.
Magnetisation transfer is observed from H8 to C2, C3, C7 and C8, and from H1 to C2 ( Figure 3). In particular, the former suggests the formation of an intramolecular hydrogen bond between the COOH (and its hydrogen H8) and the carboxylate group. Indeed, for an intermolecular bond, the distance would have been greater than 3.0 Å, which is incompatible with the presence of a correlation. This hypothesis is strongly supported by the 1 H MAS analysis ( Figure 2a) reported above. Furthermore, the higher intensity of the H8/C3 correlation with respect to the H8/C2 one suggests that the carboxylic group is in the meta (C3-C8) rather than in the ortho (C2-C7) position. Although qualitative, this evidence is supported by the use of the off-resonance CP (LG-CP), which avoids spin diffusion and guarantees that the polarisation transfer occurs by heteronuclear dipolar interaction only.
All these NMR data are in perfect agreement with the SCXRD structure, which shows QA in the zwitterionic form, with the carboxylate group in the ortho position.

Dipicolinic Acid
In the DPA 13 C CPMAS spectrum (Figure 4b), only four signals are present over seven carbon atoms, implying a high level of symmetry of the molecule in the unit cell. Indeed, the resonance at 171.2 ppm, which integrates for two, is ascribable to two carboxylic groups. Therefore, we can assess the presence of one independent molecule in the unit cell (Z = 1). Furthermore, the carboxylic groups are probably involved in an R 2 2 (8) homosynthonic hydrogen-bond pattern. Magnetisation transfer is observed from H8 to C2, C3, C7 and C8, and from H1 to C2 ( Figure 3). In particular, the former suggests the formation of an intramolecular hydrogen bond between the COOH (and its hydrogen H8) and the carboxylate group. Indeed, for an intermolecular bond, the distance would have been greater than 3.0 Å, which is incompatible with the presence of a correlation. This hypothesis is strongly supported by the 1 H MAS analysis (Figure 2a) reported above. Furthermore, the higher intensity of the H8/C3 correlation with respect to the H8/C2 one suggests that the carboxylic group is in the meta (C3-C8) rather than in the ortho (C2-C7) position. Although qualitative, this evidence is supported by the use of the off-resonance CP (LG-CP), which avoids spin diffusion and guarantees that the polarisation transfer occurs by heteronuclear dipolar interaction only.
All these NMR data are in perfect agreement with the SCXRD structure, which shows QA in the zwitterionic form, with the carboxylate group in the ortho position. In the DPA 13 C CPMAS spectrum (Figure 4b), only four signals are present over seven carbon atoms, implying a high level of symmetry of the molecule in the unit cell. Indeed, the resonance at 171.2 ppm, which integrates for two, is ascribable to two carboxylic groups. Therefore, we can assess the presence of one independent molecule in the unit cell (Z' = 1). Furthermore, the carboxylic groups are probably involved in an (8) homosynthonic hydrogen-bond pattern.  Furthermore, some spatial proximities highlighted in Figure 6b give some important information about the crystal packing. In detail, the detected H8/C5 and H3/C7 correlations can only refer to intermolecular proximities, not compatible with the long interatomic intramolecular distances between the involved heavy nuclei.

Dinicotinic Acid
As in the previously discussed cases, the 13 C CPMAS spectrum of DNic (Figure 7b) indicates the presence of one independent molecule in the unit cell (Z = 1), since the number of expected peaks (7) matches exactly the number of carbon nuclei in the molecule (7). Focusing on the carboxylic region, two distinct resonances are observed at 162.9 and 169.0 ppm. The peak at lower ppm values is related to a carboxyl group (COOH), while the latter can be assigned to either a carboxylate or a carboxyl group involved in a strong hydrogen bond or even an intermediate situation between a carboxylic and a carboxylate group, i.e., a continuum in which the proton is shared between the oxygen and the nitrogen atoms.
To validate the information obtained from the 13 C spectrum and to explore in more detail the nature of this hydrogen bond, we also performed and analysed 1D 1 H MAS and 2D 1 H DQ MAS spectra (Figure 7a and Figure S6 in the Supplementary Materials). As for the other two investigated systems, the hydrogen-bond region exhibits one signal at 12.8 ppm (H7), consistent with a COOH proton involved in a hydrogen bond; the highfrequency resonance at 19.6 ppm, associated to H1, agrees with the presence of a strong hydrogen bond (see Table 1).   Additionally, we looked at the 15 N CPMAS spectrum to precisely determine the protonation state of the compound in its crystal structure (i.e., zwitterionic, neutral or continuum). The 15 N spectrum displays a resonance at 252.9 ppm, which is an intermediate value between those of QA (205.3 ppm) and DPA (316.0 ppm), and usually is associated to a neutral pyridinic nitrogen involved in a hydrogen bond [37]. In this specific instance, no definitive hypothesis could thus be made around the protonation state of DNic based only on the 1D spectra, which led to the acquisition of the 2D 1 H-13 C correlation experiments and N-H distance measurements. Furthermore, some spatial proximities highlighted in Figure 6b give some important information about the crystal packing. In detail, the detected H8/C5 and H3/C7 correlations can only refer to intermolecular proximities, not compatible with the long interatomic intramolecular distances between the involved heavy nuclei. ber of expected peaks (7) matches exactly the number of carbon nuclei in the molecule (7). Focusing on the carboxylic region, two distinct resonances are observed at 162.9 and 169.0 ppm. The peak at lower ppm values is related to a carboxyl group (COOH), while the latter can be assigned to either a carboxylate or a carboxyl group involved in a strong hydrogen bond or even an intermediate situation between a carboxylic and a carboxylate group, i.e., a continuum in which the proton is shared between the oxygen and the nitrogen atoms. To validate the information obtained from the 13 C spectrum and to explore in more detail the nature of this hydrogen bond, we also performed and analysed 1D 1 H MAS and 2D 1 H DQ MAS spectra (Figure 7a and S6 in the Supplementary Materials). As for the other two investigated systems, the hydrogen-bond region exhibits one signal at 12.8 ppm (H7), consistent with a COOH proton involved in a hydrogen bond; the high-frequency resonance at 19.6 ppm, associated to H1, agrees with the presence of a strong hydrogen bond (see Table 1).
Additionally, we looked at the 15 N CPMAS spectrum to precisely determine the protonation state of the compound in its crystal structure (i.e., zwitterionic, neutral or continuum). The 15 N spectrum displays a resonance at 252.9 ppm, which is an intermediate value between those of QA (205.3 ppm) and DPA (316.0 ppm), and usually is associated to a neutral pyridinic nitrogen involved in a hydrogen bond [37]. In this specific instance, no definitive hypothesis could thus be made around the protonation state of DNic based only Thus, these proximities provide an idea of the spatial arrangement of the molecules in the unit cell. The intensities of the correlations between H1 and C2 and C6 suggest that H1 may be very close to the pyridinic nitrogen, which could even be protonated, in agreement with the 1D 13 C data. Indeed, the strong H1/C8 correlation is fully consistent with the formation of a hydrogen bond between the carboxylic group (C8) and N1.
The presence of the H7/C3 correlation, most likely due to an intramolecular proximity, and the absence of a similar correlation between H8 and C5 led to the conclusion that the molecule in the unit cell might be zwitterionic, with C7 corresponding to a neutral carboxylic moiety. As for C8, from all the SSNMR spectra shown above, it is still not clear whether the molecule is to be considered properly zwitterionic or whether the proton is shared. Indeed, this last hypothesis would agree with the ND crystal structure at room temperature, in which a neutral-zwitterionic continuum is observed (where "neutral" stands for a species without charge separation).
To clearly define the position of the proton along the axis of this hydrogen bond and resolve this doubt, we exploited the NMR technique to its full potential and a 14 N-1 H PM-S-RESPDOR experiment was performed to precisely measure the N-H distance. Indeed, it has been proved that this sequence is able to extract reliable N-H distances at natural abundance [40][41][42], having been also successfully tested on real samples [22]. Details of the experimental procedure for the extraction of the N-H distance are reported in the Supplementary Materials.
The N-H distance is extracted by matching the experimental and analytical fitting of the ∆S/S 0 fraction curve of the 1 H signal of H1 at 19.6 ppm, as assigned from the 2D long-range 1 H-13 C FSLG HETCOR SSNMR spectrum. The extracted value was obtained by considering the mixing time (τ) value up to 0.8 ms. The experimental and simulated ∆S/S 0 fraction curves are represented in Figure 9 as black dots and solid red lines, respectively.
The best fittings are obtained with an N-H distance of 1.31 Å which is highly comparable to the value measured in the ND crystal structure of 1.308 Å [36]. This measurement clearly indicates that the proton is shared between the pyridinic nitrogen and the oxygen of the C8 carboxylic group, to form a neutral-zwitterionic continuum. This case proves SSNMR to be an excellent and elegant tool for precisely determining the position of protons also in ambiguous systems such as DNic.
Molecules 2023, 28, x 12 of 26 on the 1D spectra, which led to the acquisition of the 2D 1 H-13 C correlation experiments and N-H distance measurements. The 2D short-range ( Figure S7 in the Supplementary Materials) and long-range (Figure 8a) 1 H-13 C FSLG HETCOR SSNMR spectra of DNic clearly show that the H7/C3-C4-C5 and H7/C8 correlations are associated to intermolecular proximities, since the interatomic distances within the molecule would be greater than 4 Å.  A further piece of information that upholds the shared-proton nature of this hydrogen bond comes from a 13 C CPMAS spectrum of DNic recorded at 173.15 K ( Figure 10). Indeed, previous studies illustrated how in carboxylic acid/pyridine adducts the shared proton moves closer to the nitrogen site with decreasing the temperature [43,44]. The complete list of chemical shifts is reported in Table S4 in the Supplementary Materials. The low-temperature spectrum shows some small but reliable differences concerning the aromatic peaks of C2, C4 and C6. A minor shift of the C8 one to higher frequencies (Δδ = 0.3 ppm) is also observed. The direction of the shift is consistent with the low-temperature (15 K) ND structure, in which the hydrogen moves towards the nitrogen atom (N-H distance: 1.213 Å), i.e., towards a zwitterionic state. The small entity of this shift (0.3 ppm) appears sound in three different aspects: (i) the SSNMR spectrum was acquired at 173 K A further piece of information that upholds the shared-proton nature of this hydrogen bond comes from a 13 C CPMAS spectrum of DNic recorded at 173.15 K ( Figure 10). Indeed, previous studies illustrated how in carboxylic acid/pyridine adducts the shared proton moves closer to the nitrogen site with decreasing the temperature [43,44]. The complete list of chemical shifts is reported in Table S4 in the Supplementary Materials. A further piece of information that upholds the shared-proton nature of this hydrogen bond comes from a 13 C CPMAS spectrum of DNic recorded at 173.15 K ( Figure 10). Indeed, previous studies illustrated how in carboxylic acid/pyridine adducts the shared proton moves closer to the nitrogen site with decreasing the temperature [43,44]. The complete list of chemical shifts is reported in Table S4 in the Supplementary Materials. The low-temperature spectrum shows some small but reliable differences concerning the aromatic peaks of C2, C4 and C6. A minor shift of the C8 one to higher frequencies (Δδ = 0.3 ppm) is also observed. The direction of the shift is consistent with the low-temperature (15 K) ND structure, in which the hydrogen moves towards the nitrogen atom (N-H distance: 1.213 Å), i.e., towards a zwitterionic state. The small entity of this shift (0.3 ppm) appears sound in three different aspects: (i) the SSNMR spectrum was acquired at 173 K The low-temperature spectrum shows some small but reliable differences concerning the aromatic peaks of C2, C4 and C6. A minor shift of the C8 one to higher frequencies (∆δ = 0.3 ppm) is also observed. The direction of the shift is consistent with the lowtemperature (15 K) ND structure, in which the hydrogen moves towards the nitrogen atom (N-H distance: 1.213 Å), i.e., towards a zwitterionic state. The small entity of this shift (0.3 ppm) appears sound in three different aspects: (i) the SSNMR spectrum was acquired at 173 K and not at 15 K; (ii) at 15 K the ND still shows an intermediate and not a complete zwitterionic character, i.e., N-H distance = 1.213 Å rather than the usual 1.128 Å expected for N + -H as extrapolated from a CSD survey (CSD version 5.40, updated in September 2019 on the N-H and N-D distances of pyridine-carboxylic acid interactions in ND structures); (iii) at 173 K, the hydrogen may still have some dynamic features and NMR could be observing an averaged situation.

CSP
Thanks to the information obtained by SSNMR, we were able to define the correct input for the CSP calculation of QA and DPA (i.e., Z = 1 for both and zwitterionic and non-zwitterionic character in the solid state, respectively). In the case of QA we started from the zwitterionic structure with the carboxylate group in C7 and the carboxylic group in C8. Concerning DNic, since from SSNMR data the proton seemed to be shared between the carboxylic group and the pyridinic nitrogen, but with a continuous shift towards the nitrogen with decreasing the temperature, we used the zwitterionic form as molecular input for the CSP calculation.
The individuals (IDs) generated by the CSP were clustered based on the degree of overlap using the Mercury utility Crystal Packing Similarity. The best IDs with Z = 1 were identified in a range of 10 kJ/mol, i.e., the energy range in which polymorphs can be found [45], and subsequently re-optimised at DFT level with QE, also performing the chemical shifts calculation.

CSP of QA
The CSP calculation produced 1064 IDs. The best IDs, in the range of 10 kJ/mol, are reported in Table 2. After the DFT optimisation step, only two IDs (315 and 630) were included in the prefixed energy range of 10 kJ/mol. For these IDs, SSNMR chemical shifts were calculated and the 13 C and 1 H RMSEs between computed and experimental chemical shifts were evaluated, as reported in Table 2. Table 2. Energy differences (∆E, kJ/mol) and space groups of the best predicted structures of QA optimised with the Dreiding FF (top); energy differences (∆E, kJ/mol), 13  ID 315 seemed to be slightly thermodynamically favoured, but the small energy difference and its higher 13 C and 1 H RMSE values indicate that ID 630 should be preferred as a candidate for the final structure. A comparison of cell parameters of the experimental and the predicted crystal structure is reported in Table 3. Experimental and computed (ID 630) cell volume, axes lengths, and angles show an overall remarkable agreement.
The overlay of ID 630, the one selected according to the SSNMR RMSEs, and the experimental structure of QA, shown in Figure 11, points out the almost perfect correspondence between hydrogen-bond patterns and molecular arrangements. A remarkably low RMSE (0.132 Å) of the overlay of these two molecular packing is observed. The overlay of ID 630, the one selected according to the SSNMR RMSEs, and the experimental structure of QA, shown in Figure 11, points out the almost perfect correspondence between hydrogen-bond patterns and molecular arrangements. A remarkably low RMSE (0.132 Å) of the overlay of these two molecular packing is observed.

CSP of DPA
DPA crystallises in the neutral form with Z' = 1, as revealed by SSNMR; thus, this information was used as CSP input. A total of 1089 IDs were produced by USPEX, from which the five best IDs were extracted (Table S5 in the Supplementary Materials) and reoptimised using QE. Of these, only two IDs (Table 4) met the selection criteria described above. From 13 C and 1 H RMSEs and energy evaluation it is clear that the most encouraging structure is ID 80, displaying a better RMSE value as well as a lower energy.

CSP of DPA
DPA crystallises in the neutral form with Z = 1, as revealed by SSNMR; thus, this information was used as CSP input. A total of 1089 IDs were produced by USPEX, from which the five best IDs were extracted (Table S5 in the Supplementary Materials) and re-optimised using QE. Of these, only two IDs (Table 4) met the selection criteria described above. From 13 C and 1 H RMSEs and energy evaluation it is clear that the most encouraging structure is ID 80, displaying a better RMSE value as well as a lower energy.
ID 80 was compared with the experimental structure of DPA, showing a perfect agreement in terms of spatial molecular arrangement and hydrogen-bond pattern. The overlay of the experimental and the predicted structures is represented in Figure 12, where the hydrogen-bond pattern and the molecular layers are shown. The cell parameters of the experimental and predicted crystal structure are shown in Table 5.  ID 80 was compared with the experimental structure of DPA, showing a perfect agreement in terms of spatial molecular arrangement and hydrogen-bond pattern. The overlay of the experimental and the predicted structures is represented in Figure 12, where the hydrogen-bond pattern and the molecular layers are shown. The cell parameters of the experimental and predicted crystal structure are shown in Table 5.

CSP of DNic
Two preliminary CSP calculations were carried out employing USPEX with the Dreiding FF, using both the neutral and the zwitterionic DNic molecule as molecular input. In the first case, no plausible crystal structure was found. In the latter case, we found quite a good structure within the best predicted individuals, with space group P2 1 /c (Z = 1), reasonable cell parameters and hydrogen-bond network. The 1 H, 13 C, and 15 N RMSE values of the computed and experimental SSNMR chemical shifts were 1.9, 1.7, and 47.5 ppm, respectively. The comparison with the experimental crystal structure is almost perfect but for a mismatch of the formed hydrogen-bonded ring (see Figure S8 in the Supplementary Materials). For this reason, and because of the uncertainty of the proton position, we performed a third CSP calculation but employing a DFT method for the geometry optimisation rather than the molecular mechanics (MM) method. USPEX produced 1108 structures that were grouped on the base of their crystal packing similarity. Of these, only two were selected as best IDs. The relative energies and 13 C and 1 H chemical shifts RMSEs with experimental values are reported in Table 6. Since SSNMR calculations are performed at 0 K, computed 13 C chemical shifts were also compared with the experimental ones obtained at 173.15 K; as expected, in this case, we observed lower 13 C RMSE values, as shown in Table 6. Table 6. Energy differences (∆E, kJ/mol) and 13 C and 1 H chemical shift RMSEs (ppm) for the best predicted structures of DNic. The 13 C RMSEs were computed using both room-and low-temperature experimental chemical shifts. From relative energies and chemical shifts RMSEs it is not possible to unambiguously select the correct crystal structure of DNic.
As can be observed in Figure 13a, both structures show molecular arrangements and the formation of an R 4 4 (24) hydrogen-bonded ring consistent with the information obtained from 2D SSNMR spectra (Figure 8), in particular from the H7/C4-C5 and H7/C8 correlations. The crystal structures of both ID 715 and ID 791 are characterised by planar sheets, which differ for the relative orientation of the molecules in two neighbouring layers, indicated as A and B in Figure 13. While layer A is the same in both IDs, layer B differs in the molecular orientation (Figure 13b).
Since ID 715 and ID 791 are very similar in terms of energy and chemical shift RMSEs, we relied on the ability of the 1 H DQ MAS experiment in probing 1 H-1 H proximities, which strongly reflect the crystal packing, for selecting the best candidate. The presence of a weak correlation between H1 and H1 of two neighbouring molecules in the 1 H DQ MAS spectrum of DNic ( Figure S6 in the Supplementary Materials) seemed to point to ID 715 as the best one since it is characterised by the smallest distance (3.23 Å) between these two atoms with respect to ID 791 (3.77 Å). The selection was confirmed by the comparison among the simulated XRD powder patterns of the experimental (15 K) and the predicted crystal structures (Figure 14). The powder pattern of ID 715 is significantly much more consistent with the experimental one; the small difference in the peak positions is probably due to tiny variations of the cell parameters of the experimental and computed structures, while peak intensity is certainly comparable. Thus, ID 715 was selected as the correct crystal structure. Table 7 reports the cell parameters of the experimental and predicted crystal structures of DNic, which are in perfect agreement, as well as the overlay of the two structures (Figure 13c,d), which displays an RMSE of only 0.063. Since ID 715 and ID 791 are very similar in terms of energy and chemical shift RMSEs, we relied on the ability of the 1 H DQ MAS experiment in probing 1 H-1 H proximities, which strongly reflect the crystal packing, for selecting the best candidate. The presence of a weak correlation between H1 and H1 of two neighbouring molecules in the 1 H DQ MAS spectrum of DNic ( Figure S6 in the Supplementary Materials) seemed to point to ID 715 as the best one since it is characterised by the smallest distance (3.23 Å) between these two atoms with respect to ID 791 (3.77 Å). The selection was confirmed by the comparison among the simulated XRD powder patterns of the experimental (15 K) and the predicted crystal structures (Figure 14). The powder pattern of ID 715 is significantly much more consistent with the experimental one; the small difference in the peak positions is probably due to tiny variations of the cell parameters of the experimental and computed structures, while peak intensity is certainly comparable. Thus, ID 715 was selected as the correct crystal structure. Table 7 reports the cell parameters of the experimental and predicted crystal structures of DNic, which are in perfect agreement, as well as the overlay of the two structures (Figure 13c,d), which displays an RMSE of only 0.063.    In this case, the use of chemical shifts RMSEs was not sufficient to determine which of the two predicted structures was the correct one since they differed only for the orientation of the molecules in the alternating parallel layers. Indeed, 13 C and 1 H RMSEs are less sensitive to this kind of structural variation; thus, in this case, the comparison with experimental SSNMR data proves marginal in discriminating between the two predicted structures.

SSNMR Experiments
All SSNMR spectra, except for 1 H MAS spectra and the low-temperature 13 C CPMAS spectrum of DNic, were recorded at room temperature on a Bruker Avance II 400 Ultra Shield spectrometer, operating at 400.23, 100.63 and 40.56 MHz for 1 H, 13 C and 15 N, respectively. 13 C and 15 N CPMAS spectra were acquired with 4 mm zirconia rotors at a spinning speed of 12 ( 13 C) and 9 ( 15 N) kHz, using a ramp cross-polarisation pulse sequence (90 • 1 H pulse of 3.8 µs; contact time of 3 and 4-7 ms for 13 C and 15 N, respectively). 1 H-13 C 2D CP ("short range") and LG-CP ("long range") FSLG HETCOR measurements were acquired at a spinning speed of 12 kHz, with a contact time of 0.1 or 2.5 ms, to allow only for short-range or also long-range magnetisation transfer, respectively. For every spectrum, a two-pulse phase modulation (TPPM) decoupling scheme was used, with a radiofrequency field of 69.4 kHz. 1 H MAS spectra and the low-temperature 13 C CPMAS spectrum of DNic were acquired on a Jeol ECZR 600, operating at 600.17 MHz for 1 H and 150.91 MHz for 13 C. The 1 H MAS spectra for DNic were acquired at room temperature with 1 mm zirconia rotors at a spinning speed of 62.5 kHz with an echo pulse sequence (90 • -τ-180 • -τ) to remove the probe background ( 1 H 90 • pulse = 0.9 µs, τ = 27 µs). The 13 C CPMAS spectrum of DNic was acquired with a 3.2 mm zirconia rotor at 173.15 K (temperature calibrated on the 207 Pb signal of Pb(NO 3 ) 2 ) [46] at a spinning speed of 20 kHz, using a ramp cross-polarisation pulse sequence with a 90 • 1 H pulse of 1.9 µs, a contact time of 3.5 ms. For the 13 C CPMAS spectrum, a two-pulse phase modulation (TPPM) decoupling scheme was used, with a radiofrequency field of 108.5 kHz.
The 2D 1 H DQ MAS experiment was performed with the back-to-back (BABA) recoupling pulse sequence with excitation time durations of one rotor period ( 1 H 90 • = 0.9 µs).
All recycle delays used in this work are optimised by means of saturation recovery experiments. Complete experimental parameters are reported in the Supplementary Materials (Table S1).
For the PM-S-RESPDOR experiment on DNic, we used the pulse sequence reported elsewhere [40]. The 1 H radio frequency (rf) field for π/2 and π pulses was 278 kHz, while it was 125 kHz for the SR4 2 1 recoupling sequence. The length of the PM pulse was 10t R (0.16 ms) and the 14 N rf field was 80 kHz (calibrated through NH 4 Cl). To reach the steady state, prior to the PM-S-RESPDOR measurements, nine dummy scans were applied. The mixing time (τ) was varied from 0 to 1. adamantane (at 1.87 ppm), the methylenic signal of external standard glycine (at 43.7 ppm) and the signal of external standard glycine (at 33.4 ppm with reference to NH 3 ), respectively.

Crystal Structure Prediction
Molecular structures of QA, DNic, and DPA were optimised in gas phase using the program Gaussian 09 [47], employing the B3LYP functional with the optimised def2-SVP basis set [48,49], with no constraints imposed during geometry optimisations. The D3 version of Grimme's dispersion method was applied adopting the Becke−Johnson damping scheme [50]. The nature of all stationary points was confirmed by normal-mode analysis. These optimised geometries were employed as initial molecules for the CSP with USPEX. The USPEX evolutionary algorithm [51,52] (v. 10.4) by Oganov's group was used for the prediction of solid-state structures. The first generation of crystal structures was created using the random-sampling operator, while afterwards different variation operators were applied, in particular rot-mutation and lattice mutation. All the structures were sampled within a set of the most common observed space group for organic molecules, considering only one molecule in the asymmetric unit cell (Z = 1), as suggested from SSNMR spectra. For geometry optimisation steps of CSP of QA and DPA, GULP (v. 5.1) was applied, with the Dreiding [53] force field (FF). For DNic, due to the uncertainty of the protonation state (see text above), we used a DFT method for the geometry optimisation: VASP (v. 5.4.4) was employed with the included PAW-PBE pseudopotentials [54]. For each CSP calculation, only the structures resulting to be in the range of 10 kJ/mol from the lowest energy structure were taken into consideration. The best predicted structures were re-optimised at DFT level with Quantum Espresso (QE, v. 6.4.1) [55], employing the projector augmented wave (PAW) approach, with the non-local vdW-df2 method [56] and the B86r functional [57] with the SSSP set of pseudopotentials [58,59]. An energy cut-off of 60 Ry was used. For the best predicted structures, NMR calculations were performed using the Gauge Including Projected Augmented Wave (GIPAW) [60] and the PBE pseudopotentials from PS Library 1.0.0 [61] with an energy cut-off of 80 Ry, following the methodology previously described [62][63][64].

Crystal Structures Comparison and Visualisation
For the visualisation and comparison of the predicted structures, the CCDC Mercury utility (v. 2020.2) was employed, using the crystal packing similarity method. The size of the molecular cluster was set to 15, while tolerance on angles and distances was set to 40%.

Conclusions
The aim of this work was to test the CSP-NMRX method on three of the structural isomers of pyridine dicarboxylic acid with ambiguous hydrogen positions, namely QA, DPA and DNic. Indeed, each of these molecules could be potentially zwitterionic or not in the solid state. Mono-and bidimensional SSNMR spectra (i.e., 1 H MAS, 13 C and 15 N CP-MAS, 1 H DQ MAS, 1 H-13 C HETCOR and 14 N-1 H PM-S-RESPDOR) proved fundamental to determine the nature of QA, DPA and DNic in the solid state, providing exact information on the proton position, to be used as constraints in the input step of the CSP calculations. QA resulted to be zwitterionic and DPA non-zwitterionic. DNic was undoubtedly the most challenging system. SSNMR provided, through the 14 N-1 H PM-S-RESPDOR experiment, very precise indications that DNic is in a continuum at ambient conditions, while, with lowering the temperature, the migration of the proton from the carboxylic group to the pyridinic nitrogen becomes more pronounced. Furthermore, 2D SSNMR data unambiguously defined the correct isomer of QA in the unit cell, since the carboxylate could be in the ortho as well as in the meta position. All the information obtained from SSNMR experiments was used as input for the CSP calculations, allowing us to save a lot of computational time. CSP calculation provided several possible crystal structures which were selected according to the comparison of computed and experimental 1 H and 13 C chemical shifts (RMSEs). Regarding DNic, the SSNMR RMSE values were not sufficient to discriminate the correct crystal packing, due to their low sensitivity to small structural variations. In this case, the 1 H DQ MAS experiment and the comparison of the calculated diffraction patterns of the predicted individuals with that of the experimental crystal structure were employed to pinpoint the right one. We strongly believe that the CSP-NMRX approach can be easily applied to a wide range of systems (from organic and organometallic to inorganic ones) which exhibit uncertain proton positions, and for which the crystal structure cannot be solved by diffraction methods, thus proving to be of great interest to the scientific community.
Supplementary Materials: The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/molecules28041876/s1, Figure S1: 1 H MAS spectra; Figure S2 Table S1: complete SSNMR experimental parameters; Table S2: experimental and computed chemical shifts of QA; Table S3: experimental and computed chemical shifts of DPA; Table S4: experimental and computed chemical shifts of DNic; Table S5: relative energies of DPA predicted structures with the Dreiding FF.